This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A191997 #6 Mar 30 2012 18:49:34 %S A191997 1,2,32,128,512,8192,2097152,226492416,301989888,536870912, %T A191997 32212254720,8349416423424,4453022092492800,1122161567308185600, %U A191997 2294196982052290560,12235717237612216320,16314289650149621760,58731442740538638336000,51166832915557261718323200 %N A191997 Denominators of partial products of a Hardy-Littlewood constant. %C A191997 The rational partial products are r(n)=A191996(n)/a(n), n>=1. %C A191997 The limit r(n), n->infinity, approximately 1.3203236, is the constant C(f_1,f_2) appearing in the Hardy-Littlewood conjecture (also called Bateman-Horn conjecture) for the integer polynomials f_1=x and f_2=x+2 (relevant for twin primes). See the Conrad reference Example 1, p. 134, also for the original references. %D A191997 Keith Conrad, Hardy-Littlewood constants, pp. 133-154 in: Mathematical properties of sequences and other combinatorial structures, edts. Jong-Seon No et al., Kluwer, Boston/Dordrecht/London, 2003. %H A191997 Wolfdieter Lang, <a href="/A191997/a191997.txt">Rationals and limit.</a> %F A191997 a(n) = denominator(r(n)), with the rational r(n):=2*product(1-1/(p(j)-1)^2,j=2..n), with the primes p(j):=A000040(j). %e A191997 The rationals r(n)(in lowest terms) are 2, 3/2, 45/32, 175/128, 693/512, 11011/8192,... %Y A191997 A191996, A191998/A191999 %K A191997 nonn,easy,frac %O A191997 2,2 %A A191997 _Wolfdieter Lang_, Jun 21 2011